Last week, the Muse frontman told The Observer that he was unhappy with conservative politicians in the US asking to play his music.
Beck - long known for his right-wing politics - wrote an open letter to Bellamy explaining his position, saying that the meaning of Muse's lyrics appeal to people questioning the make-up of society.
He wrote: "To me your songs are anthems that beg for choruses of unity and pose the fundamental question facing the world today - can man rule himself?"
Beck continued: "In the Venn Diagram of American politics, where the circles of crimson and blue overlap, there's a place where you and I meet. It's a place where guys who cling to their religion, rights and guns, connect with godless, clinched-fist-tattoo guys.
"You seem to have a pretty good grasp of comparative US and European politics, but maybe there's a pattern that you're underestimating... America... does not rely on leaders - we rely on the individual. Our country was built on the principles of mercy, justice, and charity - we ultimately believe that man left alone is good.
"American Libertarians understand that smaller government gives people freedom - the freedom to earn or lose, eat or starve, own or sell. The potential for wild success and happiness is tempered by an equal chance of failure. And it is all up to the individual to take control of their destiny."
Beck argued that US conservative politicians are often "confused", and that they simply want to increase freedom and creativity.
He closed the letter by saying: "Matthew, I realise that converts are pretty hard to come by when the stakes are so high and the spotlight so bright, but I thank you for singing words that resonate with man in his struggle to be free.
"I wish I could leave well enough alone and just be quiet... 'but I've had recurring nightmares that I was loved for who I am and missed the opportunity to be a better man'.
"Good luck on the new record."
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Watch the video for Muse's 'Madness' below: